For the first time since the US launched the Middle East peace talks last summer, the Palestinian leadership may be sensing it has a tiny bit of leverage.

Barack Obama met the Palestinian president Mahmoud Abbas in Washington last week in what Palestinian officials called a “candid and difficult” meeting. The US president hoped to dissuade Abbas from walking away when the original negotiations’ timetable ends in a month.

The US president and his secretary of state, John Kerry, want their much-delayed “framework agreement” to provide the pretext for spinning out the stalled talks for another year. The US outline for peace is now likely to amount to little more than a set of vague, possibly unwritten principles that both sides can assent to.

The last thing the US president needs is for the negotiations to collapse, after Kerry has repeatedly stressed that finding a solution to the Israeli-Palestinian conflict is imperative.

The US political cycle means Obama’s Democratic party is heading this autumn into the Congressional mid-term elections. A humiliating failure in the peace process would add to perceptions of him as a weak leader in the Middle East, following what has been widely presented as his folding in confrontations with Syria and Iran.

Renewed clashes between Israel and the Palestinians in the international arena would also deepen US diplomatic troubles at a time when Washington needs to conserve its energies for continuing negotiations with Iran and dealing with the fallout from its conflict with Russia over Crimea.

Obama therefore seems committed to keeping the peace process show on the road for a while longer, however aware he is of the ultimate futility of the exercise.

In this regard, US interests overlap with those of Israeli prime minister Benjamin Netanyahu. Israel has been the chief beneficiary of the past eight months: diplomatic pressure has largely lifted; Israeli officials have announced an orgy of settlement building in return for releasing a few dozen Palestinian prisoners; and the White House has gradually shifted ground even further towards Israel’s hardline positions.

The Palestinians, on the other hand, have nothing to show for their participation, and have lost much of the diplomatic momentum gained earlier by winning upgraded status at the United Nations. They have also had to put on hold moves to join dozens of international forums, as well as the threat to bring Israel up on war crimes charges at the International Criminal Court.

Abbas is under mounting pressure at home to put an end to the charade, with four Palestinian factions warning last week that the Kerry plan would be the equivalent of national “suicide”. For this reason, the White House is now focused on preventing Abbas from quitting next month – and that requires a major concession from Israel.

The Palestinians are said to be pushing hard for Israel’s agreement to halt settlement building and free senior prisoners, most notably Marwan Barghouti, who looks the most likely successor to Abbas as Palestinian leader.

Some kind of short-term settlement freeze – though deeply unpopular with Netanyahu’s supporters – may be possible, given the Israeli right’s triumph in advancing settlement-building of late. Abbas reportedly presented Obama with “a very ugly map” of more than 10,000 settler homes Israel has unveiled since the talks began.

Setting Barghouti free, as well as Ahmad Saadat, whose PLO faction assassinated the far-right tourism minister, Rehavam Zeevi, in 2001, would be an even harder pill for the Israeli government to swallow. Cabinet ministers are already threatening a mutiny over the final round of prisoner releases, due at the end of the week. But Israeli reports on Sunday suggested Washington might consider releasing Israeli spy Jonathan Pollard, possibly in return for Israel freeing more Palestinians, to keep the talks going.

Simmering tensions between the US and Israel, however, are suggestive of the intense pressure being exerted by the White House behind the scenes.

Those strains exploded into view again last week when Moshe Yaalon, Israel’s defence minister, used a speech to lambast Washington’s foreign policy as “feeble”. In a similar vein, he infuriated the White House in January by labelling Kerry “obsessive” and “messianic” in pursuing the peace process. But unlike the earlier incident, Washington has refused to let the matter drop, angrily demanding an explicit apology.

The pressure from the White House, however, is not chiefly intended to force concessions from Israel on an agreement. After all, the Israeli parliament approved this month the so-called referendum bill, seen by the right as an insurance policy. It gives the Israeli public, raised on the idea of Jerusalem as Israel’s exclusive and “eternal capital”, a vote on whether to share it with the Palestinians.

Washington’s goal is more modest: a few more months of quiet. But even on this reckoning, given Netanyahu’s intransigence, the talks are going to implode sooner or later. What then?

Obama and Kerry have set out a convincing scenario that in the longer term Israel will find itself shunned by the world. The Palestinian leadership will advance its cause at the UN, while conversely grassroots movements inside and outside Palestine will begin clamouring for a single state guaranteeing equality between Israeli Jews and Palestinians. Israel’s vehement and aggressive opposition on both fronts will only serve to damage its image – and its relations with the US.

An unexpected voice backing the one-state solution emerged last week when Tareq Abbas, the Palestinian president’s 48-year-old son, told the New York Times that a struggle for equal rights in a single state would be the “easier, peaceful way”.

Bolstering Washington’s argument that such pressures cannot be held in check for ever, a poll this month of US public opinion revealed a startling finding. Despite a US political climate committed to a two-state solution, nearly two-thirds of Americans back a single democratic state for Jews and Palestinians should a Palestinian state prove unfeasible. That view is shared by more than half of Israel’s supporters in the US.

That would constitute a paradigm shift, a moment of reckoning that draws nearer by the day as the peace process again splutters into irrelevance.

Jonathan Cook won the Martha Gellhorn Special Prize for Journalism. His latest books are “Israel and the Clash of Civilisations: Iraq, Iran and the Plan to Remake the Middle East” (Pluto Press) and “Disappearing Palestine: Israel’s Experiments in Human Despair” (Zed Books). His new website is www.jonathan-cook.net.